Thermodynamics of Transport Through the Ammonium Transporter Amt...

Thermodynamics of Transport Through the Ammonium TransporterAmt‑1 Investigated with Free Energy CalculationsR. Thomas Ullmann,*,† Susana L. A. Andrade,*,‡ and G. Matthias Ullmann*,†

†Structural Biology/Bioinformatics, University of Bayreuth, Universitatsstrasse 30, BGI, 95447 Bayreuth, Germany‡Institute of Organic Chemistry and Biochemistry and BIOSS Centre for Biological Signalling Studies, Albert-Ludwigs-UniversitatFreiburg, Albertstrasse 21, 79104 Freiburg, Germany

*S Supporting Information

ABSTRACT: Amt-1 from Archaeoglobus fulgidus (AfAmt-1)belongs to the Amt/Rh family of ammonium/ammonia trans-porting membrane proteins. The transport mode and the precisemicroscopic permeation mechanism utilized by these proteins areintensely debated. Open questions concern the identity of thetransported substrate (ammonia and/or ammonium) and whetherthe transport is passive or active. To address these questions, westudied the overall thermodynamics of the different transportmodes as a function of the environmental conditions. Then, weinvestigated the thermodynamics of the underlying microscopictransport mechanisms with free energy calculations within a continuum electrostatics model. The formalism developed for thispurpose is of general utility in the calculation of binding free energies for ligands with multiple protonation forms or otherbinding forms. The results of our calculations are compared to the available experimental and theoretical data on Amt/Rhproteins and discussed in light of the current knowledge on the physiological conditions experienced by microorganisms andplants. We found that microscopic models of electroneutral and electrogenic transport modes are in principle thermodynamicallyviable. However, only the electrogenic variants have a net thermodynamic driving force under the physiological conditionsexperienced by microorganisms and plants. Thus, the transport mechanism of AfAmt-1 is most likely electrogenic.

■ INTRODUCTION

Amt-1 from Archaeoglobus fulgidus (AfAmt-1) belongs to thewidespread family of Amt/Rh transmembrane transportproteins. The ammonium transport (Amt) proteins supplymicroorganisms and plants with ammonium as the mostdirectly utilizable nitrogen source.1−11 The human Rhesus (Rh)proteins are implicated in ammonium excretion and pHregulation functions.11−13

The precise molecular mechanism of substrate conductionthrough Amt/Rh proteins is not yet known. It is debatedwhether the uncharged ammonia or the charged ammoniumion is the species that is actually translocated by theproteins.2−11,14 Traditionally, it was thought that the trans-ported species is NH4

+.1 This opinion was grounded on severallines of evidence. First, the pKa value of 9.25 makes NH4

+ muchmore abundant than NH3 at physiological pH values around7.0. Second, lipid membranes possess a significant permeabilityfor the apolar NH3 molecule, which seemed to make adedicated transport protein unnecessary. Third and possiblymost important, the charge carried by the ammonium ionmakes it possible to drive its electrogenic transmembranetransport by the electric transmembrane potential. Thispossibility would enable a cell to take up ammonium also atvery low concentrations of ammonium in the extracellularmedium and to compensate the loss of ammonia through

unspecific permeation of the cell membrane in a process calledcyclic retention.1

The assumption of an active transport mechanism was calledinto question by some physiological experiments whoseinterpretation led to the hypothesis that Amt/Rh proteinsactually facilitate the passive, electroneutral transport of theuncharged ammonia molecule.11,15,16 These experiments weresupported by the first X-ray crystal structures of AmtB fromEscherichia coli (EcAmtB) that revealed a transmembrane porewith a hydrophobic central region whose permeation by thecharged ammonium ion was considered to be thermodynami-cally prohibitive.8,11,16,17 According to this hypothesis, NH4

+

would be recruited at the extracellular side leaving the protonbehind in the extracellular phase. The resulting ammoniamolecule would then permeate the transmembrane pore and bereprotonated at the intracellular side.However, as noted in our earlier work, an electroneutral

uniport of NH3 poses the bioenergetic problem of how a cellcan retrieve ammonia/ammonium at low extracellular concen-trations of the substrate.4,18 Reports of membrane potentialdependent uptake currents in plant and microbial Amts supportthe view of an electrogenic transport that would involve NH4

+

Received: June 3, 2012Revised: July 13, 2012Published: July 17, 2012

Article

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© 2012 American Chemical Society 9690 dx.doi.org/10.1021/jp305440f | J. Phys. Chem. B 2012, 116, 9690−9703

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either in an uniport of NH4+ or a symport of NH3 and H

+.19−27

A membrane potential dependence of the ammonium uptakeactivity was also reported for Rh type transporters,28−30 butpartly discarded as too weak to be significant.28,29 The findingthat the transport activity of the Rh proteins was stimulated byan extracellular alkalinization led to the interpretation that NH3must be involved in either a uniport of NH3

11,13,28,29 or asymport of NH3 and NH4

+.30 A summarizing scheme of thepossible transport mechanisms considered to date4,5,31 is shownin Figure 1.4

Figure 2 shows the structure of one monomer within theAfAmt-1 trimer highlighting the transmembrane pore andputative intermediate sites passed by the permeant.18 Thetransmembrane pore can be subdivided into a centralhydrophobic pore lumen and two wider and less hydrophobicvestibule regions at the intracellular and extracellular ends ofthe pore. The extracellular vestibule and the pore lumen areseparated by a narrow constriction that is formed by twoconserved phenylalanine residues (F96 and F204). The so-called Phe-gate has been attributed a role in the dehydrationand subsequent deprotonation of the ammonium ion eitherdirectly at or close to the Phe-gate.5,32,33 The pore lumen islined by hydrophobic residues except for a conserved pair ofhistidine residues (H157 and H305) termed the twin-His motif.The twin-His residues are arranged in a nearly coplanargeometry, with their Nδ atoms within hydrogen-bondingdistance. A role of the twin-His motif in the conductionmechanism has been suggested based on the structural data andmutagenesis experiments. This role could either be theproviding of hydrogen bond interactions to the permeant16,34

or as transient proton acceptor in the deprotonation of theammonium ion.5,17,35

Most previous theoretical studies of substrate permeationthrough Amt/Rh proteins concentrated on different aspects ofsubstrate permeation through EcAmtB.14,32,33,36−49 One workstudied the thermodynamics of substrate permeation throughRh50 from Nitrosomonas europaea (NeRh50).50 In this work,we studied the thermodynamics of the different possibletransport mechanisms of AfAmt-1. We extend upon previoustheoretical studies by including the effects of substrate

concentration, electrochemical transmembrane gradients, pro-ton-coupled binding equilibria, and competitive binding ofdifferent ligand species. Our free energy calculations are basedon a microstate description of AfAmt-1 within a continuumelectrostatics/molecular mechanics model.51,52 Such a descrip-tion can provide valuable insight into biomolecular functionand has already been successfully applied to other membraneproteins like bacteriorhodopsin, bacterial and plant photo-synthetic reaction centers, cytochrome bc1, quinol-fumaratereductase, and cytochrome c oxidase.52−57

■ METHODSMicrostate Description of the Receptor−Ligand

System. Our model is based on a microstate description ofthe system.51,58,59 A microstate is defined by a particularinstance occupied by each site. The term instance describes thecombination of a particular set of atomic partial charges, aparticular number of bound ligands of each ligand type and aparticular set of atomic coordinates. The energy of a microstaten is given by51

∑ ∑ ∑ ∑ν μ= − += = =

<

E E W( )i

i km

i k m mi

N

j

j i

i k j lnmicro

1

N

,int ,r

, ,1 1

, , ,

ssites ites

(1)

where Nsites is the number of sites and is the number ofligand types. Ei,k

int,r is the intrinsic energy of site i in instance k,where the superscript r designates the receptor environment.The stoichiometric coefficient νi,k,m indicates the number ofligands of type m bound to instance k of site i and μm is theelectrochemical potential of this ligand in the adjacent solution.

Figure 1. Mechanistic scheme of transport modes that could beoperative in AfAmt-1.4 (a) At physiological pH values ammonium willbe almost exclusively in the cationic form, such that translocation ofNH3 implies extracellular deprotonation and intracellular reprotona-tion. Electrogenic transport of ammonium is either a net uniport ofNH4

+ as depicted in panel b or a symport of NH3/H+ as depicted in

panel c. Both electrogenic transport modes result in a net transport ofNH4

+. During a uniport the ammonium ion is translocated as an intactentity. In contrast, during a symport the ammonium ion is separatedinto an ammonia molecule and a proton, which may be translocatedalong different routes, and recombined on the inner side of themembrane.

Figure 2. Structure of Amt-1 from Archaeoglobus fulgidus (AfAmt-1).The extracellular side is shown at the top and the intracellular side atthe bottom. The figure shows a single monomer. The boundaries ofthe membrane core (yellow) and headgroup regions (green) areindicated by the bars on the right-hand side of the plot. The whiteregions at the top and the bottom denote the solvent phases. Thelight-gray outer region of Amt-1 is a projection of the solventinaccessible volume of the transporter trimer into a planeperpendicular to the membrane. The darker inner region is aprojection of a thin slice of Amt-1 into the same projection plane.The slice plane is slightly tilted with respect to the membrane normalto follow the course of the transmembrane pore. The positions of theinvestigated permeant positions (blue), the twin-histidine motif (cyan)and the Phe-gate (light yellow) are indicated.

The Journal of Physical Chemistry B Article

dx.doi.org/10.1021/jp305440f | J. Phys. Chem. B 2012, 116, 9690−97039691

Wi,k,j,l is the interaction energy of sites i and j in their respectiveinstances k and l.The intrinsic energy in the receptor environment Ei,k

int,r iscalculated relative to the intrinsic energy of an appropriatemodel compound in solution Ei,k

int,m60,61

= + ΔE E Ei k i k i k,int ,r

,int ,m

,int

(2)

The intrinsic energy shift ΔEi,kint upon transfer from the solutionto the receptor environment is obtained from a continuum-electrostatics/molecular mechanics model.51,52,62,63

The definition of an equilibrium state requires that each sitebinds its ligands exclusively from one of the membrane sidesonly and that no transfer of ligands takes place between themembrane sides.62,63 Thus, the connectivity of each site to oneof the membrane sides has to be determined. In thetransmembrane pore of AfAmt-1, the Phe-gate separates themembrane sides and thus defines the connectivity of the pore-lining residues. The permeant sites Am1a and Am1b areconnected to the extracellular side. The rest of the permeantsites and the twin-His residues are connected to theintracellular side. All other sites are assigned to eithermembrane side based on their exposure to either solventphase or their involvement in hydrogen bonding networks(Table S1 of the Supporting Information).An additional complication arises if a ligand can undergo

binding reactions with other ligands, e.g., if the ligand itself isprotonatable. In such a case all of the binding equilibriainvolving the macromolecular receptor, the ligand, and theproton are coupled. The corresponding expressions for theligand chemical potentials in our case are given below.Electrochemical Potentials of the Ligands. The

chemical potential of a ligand i is given by

μ μ β= ° + − alni i i1

(3)

where μi° and ai are the standard chemical potential and theactivity of the ligand, respectively. The electrochemicalpotential of the ligand i extends the chemical potential by theenergy of the ligand in the electrostatic potential of thesurrounding solution

μ μ ψ = + ΘΔz Fi i i (4)

where zi is the formal charge of the ligand, F is the Faradayconstant, and Δψ is the electric transmembrane potential. Byconvention, the Heaviside step function Θ adopts a value of 0 ifthe ligand resides in the extracellular phase and a value of 1 ifthe ligand resides the intracellular phase.64,65

In our case, there is a total of six different ligand speciescomprising the proton and the permeant species ammonia,ammonium, hydroxyl ion, water, and hydronium ion. Thereaction equations for the corresponding protonation equilibriaare given by

+ ⇌+ +NH H NH3 4 (5)

and

+ ⇌ + ⇌− + + +OH 2H H O H H O2 3 (6)

The equilibrium condition demands that the sum of theelectrochemical potentials of all species is equal for each stageof the protonation equilibria eqs 5 and 6. Thus, we can writethe electrochemical potential of each ligand species as the sumof the electrochemical potentials of the fully deprotonatedligand and of the protons bound by the species

μ μ μ = + + +NH NH H4 3 (7)

μ μ μ = + − +H O OH H2 (8)

μ μ μ = + + − +2H O OH H3 (9)

Consequently, there are three independent ligand electro-chemical potentials (μH+, μOH−, and μNH3

) for each membraneside.The activity of the proton aH+ is given by the definition of

the pH as

≡ −+a 10H

pH(10)

Similar to the pH, we define the functions pO and pN, asmeasures of the total activity of all water and ammoniaprotonation forms, respectively

+ ≡ −+a a 10NH NH

pN3 4 (11)

+ + ≡ −− +a a a 10OH H O H O

pO2 3 (12)

If we assume that the activity coefficients of all protonationforms are reasonably close to a value of 1.0, pN and pO will beindependent of the pH value. With this assumption, we canexpress pN and pO as functions of the total concentration of allammonia and water species, respectively

≈ −+

°

+⎡⎣⎢

⎤⎦⎥

c c

cpN log10

NH NH3 4

(13)

≈ −+ +

°

− +⎡⎣⎢

⎤⎦⎥

c c c

cpO log10

OH H O H O2 3

(14)

where the standard concentration is, by definition, given by c°≡ 1 mol/L. Our assumption should be fulfilled reasonably wellunder physiologically relevant conditions, i.e., for smallconcentrations of ammonia and ammonium cNH3

+ cNH4+ ≪ 1

mol/L and pH values far from the extreme ends of the pHrange. The activities of the individual protonation forms ofammonia and water can then be expressed as functions of pNand pO. The activity of NH3 is given by

β μ μ μ=

+ − ° − ° −

−

+ +a

101 exp[ ( )]NH

pN

NH NH H3

4 3 (15)

The activity of the OH− ion is given by

β μ μ μ

β μ μ μ

= + − ° − ° −

+ − ° − ° −

−− − +

+ − +

{}

a 10 / 1 exp[ ( )]

exp[ ( 2 )]

OHpO

H O OH H

H O OH H

2

3 (16)

The total chemical potentials of the ammonia and the hydroxylion can be calculated via eq 3. The chemical potentials of theother permeant species follow from eqs 7−9. A detailedderivation of eqs 15 and 16 can be found in section A of theSupporting Information. Plots of the chemical potential of allpermeant species as a function of the pH value of the solutioncan be found in Figure S1 of the Supporting Information. Thestandard chemical potentials of the permeant species areavailable from experiment (see Table S4 of the SupportingInformation). In our calculations, we assume the totalconcentration of all water species to be fixed at 55.5 mol/Las calculated from the density and the molecular weight ofwater (ρH2O = 1 kg/L, MH2O = 18.015 g/mol).



Simulation Setup. Our simulations are based on the crystalstructure of AfAmt-1 in the native form (PDB code 2B2F).18

Hydrogen atoms were added with HBUILD66 in CHARMM67

and their positions were subsequently energy minimized usingthe CHARMM force field.68 The intrinsic energies andinteraction energies were computed from a continuumelectrostatics/molecular mechanics model implemented in ourprogram GCEM69 based on our modified version of the MEADlibrary.55,70 All MC simulations were carried out with ourprogram suite GMCT.51 Equilibrium probabilities of bindingforms for individual sites were computed with the MetropolisMC method.71 Free energy calculations were performed withthe free energy perturbation method72 in our recentlypresented generalization73 combined with the Bennett accept-ance ratio method.74 Details of our computational method arespecified in the remaining parts of this section.Structure Preparation. The structure of AfAmt-1 in the

native form (PDB code 2B2F) was used as basis for ourcalculations.18 Hydrogen atoms were added with HBUILD66 inCHARMM67 and their positions were subsequently energyminimized using the CHARMM force field as describedbelow.68 Two additional rotamer positions were added foreach hydroxyl or sulfhydryl hydrogen atom by varying thecorresponding torsion angle in steps of 120°. Four alternativehydrogen positions for protonated forms of carboxylic acidswere added to represent the syn and trans configurations of thedissociable proton at each carboxyl oxygen atom. Thecorresponding angles and bond lengths were taken from ref 69.The positions of the permeant sites (see Figure 2) were

determined from putative binding sites obtained fromexperimental and theoretical studies at AfAmt-118 and theclose homologue EcAmtB.16,17,32,33,48 Am1a corresponds to theammonium recruitment site between W137 and S208 identifiedin the crystallographic studies.16−18,35 This recruitment site hasalso been verified in several independent MD studies ofEcAmtB.32,33,36,37,39,41,44,47,48 Am1b was modeled based onobservations in MD simulations of EcAmtB, where ammoniumwas sandwiched by the side chains of the two phenylalanineresidues forming the Phe-gate.32,33,39,49 Similar conformationsare also observed in computational studies of a complex formedby ammonium and two benzene molecules in aqueoussolution.75 This binding site was proposed to promotedehydration of the ammonium ion and consequently tofacilitate its deprotonation either directly at this site or atAm2.32,33,39 Am2 was placed at the corresponding ammoniaposition proposed for EcAmtB (PDB 1U7G).16 Am3 and Am4were placed at xenon binding sites as found in the xenon-pressurized structure of AfAmt-1 (PDB 2B2J).18 These sitesclosely comply with the putative ammonia or water bindingsites identified in the transmembrane pore lumen of AfAmt-118

and EcAmtB.16,17,35 Am5 was placed at the position of a watermolecule (water 414) found in PDB 2B2F directly below H305at the lower end of the hydrophobic pore lumen.18 Am6 wasmodeled based on a proposed site of ammonia reprotonation inthe intracellular vestibule of EcAmtB between the side chains ofthe residues that are equivalent to D300 and S263 of AfAmt-1.16,32,33,48 The permeant positions were energy minimizedwhile setting all atomic partial charges to zero to avoid biasingtheir protonation state. The positions of the permeant heavyatoms were constrained harmonically with a force constant of0.5 kcal/(mol Å2) during the minimization. The coordinates ofall hydrogen atoms were included in the energy minimization.All protein heavy atoms except for those of the side chains of

F96 and F204 were kept fixed during the minimization.Additional rotamers were added for all permeant sites byrandomly rotating the initially generated coordinates in spaceresulting in an 8-fold increase in the number of rotamers.

Calculation of Intrinsic Energies and InteractionEnergies. The intrinsic energies and interaction energieswere computed from a continuum electrostatics/molecularmechanics model implemented in GCEM.76 We considered asingle monomer explicitly with all titratable sites, whereas theother two monomers of the trimer are represented implicitly bytheir dielectric regions. All aspartate, histidine, glutamate, lysine,arginine, cysteine, and tyrosine residues and the termini wereconsidered as protonatable sites. The permeant sites in thetransmembrane pore were modeled with binding forms for eachof the considered permeants and a ligand-free binding form asdescribed above.We used a detailed charge model with explicit hydrogen

positions for all protonatable sites. Atomic partial charges forstandard forms of amino-acid residues were taken from theCHARMM22 parameter set.68 Atomic partial charges ofnonstandard forms of amino acid residues were taken fromref 69. Model compounds of protonatable amino acids includethe entire residue plus the directly neighboring CHARMMcharge groups belonging to the backbone of the preceding andsucceeding amino acids to ensure charge neutrality and tomimic an N-formyl,N-methylamide blocked amino acidcompounds.61 The intrinsic energies of the model compoundsfor protonatable amino acid residues in aqueous solution werecalculated from pKa values of appropriate model compoundstaken from the literature52,77 as described in ref 69. Atomicpartial charges for the permeant sites were obtained fromdensity functional theory calculations with the ADF pro-gram78,79 (functionals VWN80 and BP8681,82 with a QZ4P basisset). The atomic partial charges were calculated with themultipole derived charge analysis method83 (Table S2 of theSupporting Information). The intrinsic energies for thepermeants in solution were computed from experimental data(Table S3 of the Supporting Information). The Lennard-Jonesparameters of ammonia/ammonium were taken from theCHARMM22 force field (model compounds methylamine/methylammonium).68 The Lennard-Jones parameters for thewater species were taken from the TIP3P water model.84

Conformational energies of the sites were computed usingthe CHARMM22 force field,68 and added to the intrinsicenergies. We used bonded terms involving atoms of the site,and Lennard-Jones interaction energies within the site andbetween the site and the background (i.e., parts of the proteinnot belonging to any site). Lennard-Jones interactions werealso added to the site−site interaction energies.MEAD uses a finite-difference method on cubic grids to solve

the linearized Poisson−Boltzmann equation.85,86 The dielectricconstant of the protein including the permeant sites was set to4.55 The dielectric constant of the solvent including proteincavities and unoccupied space of the transmembrane pore wasset to 80. The position of the membrane was assignedaccording to the OPM database87 and visual inspection of PDB2B2F. The dielectric constant of the membrane core,representing the hydrophobic lipid tails, was set to 2 and thedielectric constant of the polar headgroup region was set to 20.The membrane core region extends from z = −15 to +12 Å inthe coordinates defined by PDB 2B2F (see Figure 2). Theheadgroup regions have a thickness of 5 Å. The temperaturewas set to 298.15 K. The dielectric boundary between solute



and solvent was calculated using a water probe sphere of 1.4 Åradius and the atomic radii (1.0 Å for H, 1.55 Å for N, 1.7 Å forC, 1.5 Å for O, and 1.8 Å for S). The ionic strength was set to0.15 M. The thickness of the ion exclusion layer was set to 2.0Å.Electrostatic potentials were computed using the focusing

technique88 with four nested cubic grids. The grids for thecomputation of the electrostatic solvation and interactionenergies had grid spacings of 2.0 Å, 0.5 Å, 0.2 Å and 0.15 Å,respectively. The outer grid had a grid length of 101 points andwas centered on the geometric center of the protein. Thefollowing grids were centered on the geometric center of thesite. The second grid had a grid length of 241 points. The thirdgrid had a grid length of 345 points. The inner grid had a gridlength that was adjusted for each instance of each site separatelyto fit the dimensions of the site plus 15 Å in each direction. Thesame grids were used for the model compound and the site inthe protein. The grids for the computation of the electrostatictransmembrane potential64 had grid spacings of 2.0, 0.5, 0.35,and 0.2 Å, respectively. The corresponding grid lengths were121, 373, 387, and 425 points. All grids were centered on thegeometric center of the protein.Monte Carlo Simulations. All MC simulations were

carried out with our program suite GMCT.51 The temperaturewas set to 298.15 K. The interaction energy cutoffs for pair andtriplet moves were set to 1.0 and 2.0 kcal/mol.Equilibrium probabilities of binding forms for individual sites

were computed with the Metropolis MC method.71,89,90 Weused 5000 MC scans for the equilibration and 105 MC scans forthe production run.Free energy calculations were performed with the free energy

perturbation method72 in our recently presented general-ization.73 We used staging91 with nine alchemical intermediatestates evenly distributed along the transformation coordinate.The Bennett acceptance ratio method was used to minimize thestatistical error of the free energy estimates.74 Each free energycalculation consisted of multiple simulations according to therandom single-move simulation scheme.73 The number ofsimulations was increased until the statistical error of the freeenergy estimate was smaller than 0.01 kcal/mol. Each separate

simulation consisted of 1000 MC scans for equilibration and10 000 to 50 000 MC scans for production.

■ RESULTS AND DISCUSSION

Bioenergetics of Transmembrane Transport. In thissection, we study the thermodynamics of the transmembranetransport of ammonia and ammonium from an overallperspective without regard to mechanistic details. The freeenergy for the import of a permeant is given by the difference inthe electrochemical potential of the permeant between theinside phase and the outside phase64,92−94

μ μΔ = − Gtransfer in out (17)

The electrochemical potentials of ammonia and ammonium arecalculated as described in the Methods section. The electro-chemical potential of the permeant species depends on theactivity of the permeant species and the electrostatic potentialin the respective bulk solvent phase. Ammonia and ammoniumare interconvertible through protonation as described by eq 5.This protonation equilibrium leads to a pH-dependence of theactivities of ammonia and ammonium and thus of theirelectrochemical potentials (Figure S1 of the SupportingInformation). Thus, there are three factors that determine theelectrochemical potentials of ammonia and ammonium in agiven solvent phase. The first factor is the total activity ofammonium and ammonia that is measured by the pN valuedefined by eq 11. The second factor is the relative abundance ofthe two protonation forms which is determined by the pHvalue via (aNH3

/aNH4+) = 10pH−pKa, where pKa = 9.25. The third

factor is the electrostatic potential in the respective bulk solventphase determined by the electric transmembrane potential.Figure 3 shows plots of the transfer free energy for transport

of ammonia or ammonium from the extracellular phase to theintracellular phase. Figure 3a shows plots of the transfer freeenergy as a function of the intracellular pH and the proton-motive force (pmf). Figure 3b contains the corresponding plotsat a fixed intracellular pH value of 7.0 as functions of theconcentration gradient of ammonia/ammonium across themembrane and the pmf. The pmf is the electrochemicalpotential difference of the proton across the membrane

Figure 3. Transfer free energies for the import of ammonia (lower row) and ammonium (upper row). The transfer free energy is color coded (seecolor bar) and indicated by isocontours drawn in constant intervals of 1.0 kcal/mol (contour values given in kcal/mol). (a) Transfer free energies asa function of the intracellular pH and the proton-motive force. (b) Transfer free energies as a function of the transmembrane pN difference (ΔpN =pNin − pNout) and the pmf. (a and b) The pmf in the left column consists entirely of an electric transmembrane potential (pmf = ψin − ψout). Thepmf in the right column consists entirely of a transmembrane pH difference (pmf ≈ − 59 mV ΔpH).



expressed in terms of a voltage difference acting on the chargeof the proton65,92

βψ= − Δ + Δ

Fpmf

ln 10pH

(18)

where F is the Faraday constant, ΔpH = pHin − pHout, and Δψ= ψin − ψout. Here, ψ is the electrostatic potential in therespective bulk solvent phase (far from the membrane). Anegative value of the pmf corresponds to the physiologicaldirection of the pmf (ψ inside negative, outside higher protonactivity than inside), while a positive value of the pmf indicatesa nonphysiological direction of the pmf. Equation 18 provides apossibility to express the chemical component ΔpH and theelectrical component Δψ of the proton-motive in a commonunit. In this way, we can directly compare the effect of the twopmf components on the transfer free energy. Analogously toΔpH, the concentration gradient of the permeants across themembrane is expressed as ΔpN = pNin − pNout. A negativevalue of ΔpN indicates that the permeant is less abundant inthe outside phase than in the inside phase. This casecorresponds to the physiologically relevant situation formicroorganisms and plants that have to acquire ammoniumas nitrogen source at low ammonium concentrations in thesurrounding medium.1 Typical ammonium concentrationsinside the cell are ∼1 mM, whereas the ammoniumconcentration in the surrounding medium is typicallysignificantly lower.1,14,19,23,95,96

The left column of Figure 3a shows the effect of the electrictransmembrane potential on the transfer free energy. If theelectrostatic potential is lower (more negative) in the insidephase than in the outside phase, the import of the positivelycharged ammonium ion will be thermodynamically favored. Incontrast, the import of the uncharged ammonia molecule isunaffected by the electrostatic potential difference between thesolvent phases.The right column of Figure 3a shows the effect of the

transmembrane pH difference on the transfer free energy. If thepH value of the outside phase is lower than that of the insidephase, the import of NH4

+ will be thermodynamically favored.This favorable effect of the pH gradient arises because a fractionof the ammonium ions will be deprotonated in the more

alkaline inner phase leading to a free energy gain. However, themagnitude of this energy gain will be very small underphysiologically relevant conditions where, on both membranesides, the pH value is close to 7.0 and ammonium is thepredominant protonation form. In contrast, the import of NH3is hindered by a transmembrane pH difference in thephysiological direction. The free energy cost arises because apart of the imported ammonia is formed by deprotonation ofammonium at the more acidic extracellular side andreprotonated at the more alkaline intracellular side. Thus, theammonia uniport is, in this case, thermodynamically equivalentto a net antiport of an ammonium ion and a proton, where theammonium ion is imported and the proton is exported againstthe direction of the pmf.4

Figure 3b shows plots of the transfer free energy for theimport of ammonia or ammonium at a fixed intracellular pHvalue of 7.0 as a function of the transmembrane concentrationgradient of the permeant and the pmf. The permeantconcentration gradient ΔpN favors the permeant import ifthe permeant concentration in the outer phase is higher than inthe inner phase. Under physiologically relevant conditions forbacteria and plants, however, the concentration of thepermeants is lower in the outer phase than in the innerphase. Consequently, the permeant concentration gradient willactually hinder the permeant import by making a positivecontribution to the transfer free energy. This unfavorable freeenergy contribution has to be compensated by coupling thepermeant import to the pmf as a driving force. A physiologicalpmf cannot drive the net import of ammonia as can be seenfrom the lower row of Figure 3a. However, a physiological pmfcan drive the net import of ammonium as can be seen from theupper row of Figure 3a.In summary, a net uptake of nitrogen at low concentrations

of ammonia/ammonium in the extracellular medium is onlypossible as pmf-driven electrogenic import. A pmf driventransport mode couples the thermodynamically unfavorableimport of ammonia to the thermodynamically favorable importof the proton.4,96 A net electrogenic transport mode can alsoinvolve the transport of a part of the substrate as ammonia andanother part as ammonium. The import is likely predominantlydriven by the electric transmembrane potential since thetransfer free energy of ammonium is much more sensitive to

Figure 4. Electrostatic potential distribution in a cross-section through AfAmt-1 as function of the transverse position z and the lateral position y inthe projection plane. The orientation of the protein is the same as in Figure 2 and the electrostatic potentials are plotted in the same slice plane. (a)The fraction of the electric transmembrane potential (electric distance) as a function of the coordinates y and z. The fraction is color coded (seecolor bar) and indicated by isocontours. (b) The electrostatic potential under typical conditions (pH 7.0 and Δψ = −0.12 V). The structure ofAfAmt-1 was constructed by setting all sites to their most highly populated instances under the specified conditions. The electrostatic potential iscolor coded (see color bar). left: electrostatic potential contribution due to the protein charge distribution alone. right: total electrostatic potentialdue to the protein charge distribution and the electric transmembrane potential.



this component of the pmf than to the pH gradient (Figure3b). Furthermore, Δψ is also the dominant pmf component atthe membranes of bacteria1,97 and plant root cells.19

Electrostatic Potential Across AfAmt-1. In this section,we investigate the possible role of the electrostatic potential inthe transport mechanism of AfAmt-1. Figure 4 shows plots ofthe electrostatic potential distribution across AfAmt-1. Con-tributions arising from the electric transmembrane potentialand the protein charge distribution are shown separately andadded up at pH 7.0 and Δψ = −120 mV. Figure 4a shows thatthe transmembrane potential does not exhibit a simple lineardependence on the coordinate transverse to the membrane.This nontrivial dependence is caused by the complex shape ofthe molecule and the resulting distribution of the dielectricregions.64 A physiological transmembrane potential arises fromthe separation of positively and negatively charged ions by themembrane, where a net positive charge resides on theextracellular side and a net negative charge of the samemagnitude resides on the intracellular side. Thus, theelectrostatic transmembrane potential ranges from −1/2Δψin the bulk extracellular phase to +1/2Δψ in the bulkintracellular phase. The contribution of the electric trans-membrane potential to the total electrostatic potential is muchlower than the contribution of the protein electrostaticpotential for realistic values of Δψ.The protein electrostatic potential is negative in the whole

transmembrane pore region (Figure 4b). The electrostaticpotential in the vestibule regions and the lumen of the pore canthus aid in the stabilization of a positively charged permeant(see also Figures S2 to S4 of the Supporting Information). Thenegative electrostatic potential at the extracellular vestibule isalso likely to increase the rate of substrate uptake from theextracellular phase by attracting positively charged ammoniumions. The negatively charged side chain of D149 makes thelargest contribution to the negative electrostatic potential at theextracellular vestibule. A role of the equivalent residue D160 inEcAmtB in the stabilization of the ammonium ion at theextracellular vestibule has been proposed earlier by Luzhkov etal.36

Thermodynamics of Permeant Binding. In this section,we investigate the different factors that influence thethermodynamics of transferring the permeants from the bulksolvent phases to the permeant sites in the transporter pore.The free energy difference associated with this transfer can beformalized as binding free energy of a particular permeantspecies at a given permeant site in the transporter pore. Wedefined the unbound state of a permeant site by occupation ofits ligand-free binding form. The bound state is defined byoccupation of one of the forms of the permeant site with therespective permeant species bound. By comparing the bindingfree energies for the different permeant species, we caninvestigate possible implications for the transport mechanism ofAfAmt-1.Figure 5 shows the binding free energies and standard

binding free energies at all permeant sites for all permeantsconsidered (pH 7.0, Δψ = 0 mV, pN 3). The standard bindingfree energy (Figure 5a) extrapolates the binding free energy to avirtual standard concentration of 1.0 mol/L. The standardbinding free energy for the ligand species x can be calculatedfrom the binding free energy for this ligand by removing theexplicit dependence of the binding free energy on the activity ofthe ligand

β° = − −G G alnx x x,bind bind 1

(19)

In general, there is also an implicit dependence of the standardbinding free energy on the ligand activity if there are other,interacting binding sites for the same ligand.98−100 However,since the permeant sites are almost always occupied by anuncharged water molecule under physiologically relevantconditions, the interactions between the permeant sites arelimited. Consequently, the implicit dependence of the standardbinding free energy on the ligand activity is small in our case.The standard binding free energy is directly comparable to

potential of mean force profiles which are often used in MDstudies to analyze the thermodynamics of transmembranetransport. Potential of mean force profiles for the permeation ofammonia and ammonium along the transmembrane pore ofhomologues of AfAmt-1 obtained from MD studies have beenreported.32,39,48−50 We compared the potential of mean force atthe positions equivalent to our permeant sites to our standardbinding free energies. The potential of mean force profiles forthe permeation of NH3 through EcAmtB32,39,48 and NeRh5050

are comparable to the profile of our standard binding freeenergies. The corresponding profiles for the permeation ofNH4

+ obtained from the MD studies show a significantly lessfavorable thermodynamics of permeation than our standardbinding free energies. This discrepancy arises most likely fromthe presence of water in the pore lumen in our simulation andits absence in the molecular dynamics studies. In their recentwork, employing a polarizable force field, Lamoureux et al.found even more favorable standard binding free energies forammonium in the hydrophobic pore lumen than found here.49

This finding is based on the explicitly included polarizationeffect whose predicted magnitude is, however, surprisinglylarge.Upon transfer from the bulk solvent into the transmembrane

pore, the permeant is partially desolvated. This desolvationleads to a positive contribution to the binding free energy, oftentermed desolvation penalty, which disfavors binding. This effectis especially pronounced for charged permeant species. Waterpresent in the pore lumen can partially compensate for the losthydration hull and thus reduce the free energy cost fordesolvation of the charged permeant. The desolvation penaltyin our simulations is alleviated in this way because thesurrounding permeant sites are almost always occupied by

Figure 5. Standard binding free energy (a) and binding free energy (b)for different permeants at the transmembrane pore sites. The pH is setto 7.0 on both membrane sides. No pmf is applied. The pN is set to3.0 on both membrane sides. Connecting lines between the freeenergy levels are just a guide to the eye and do not imply transitionstate energies.



water. Note that the possibility of empty binding sites isincluded in our model, i.e., the water molecules are free to leavethe transporter pore. The question whether or not the porelumen is occupied by water is thus a very important point indetermining the electrostatic barrier for permeation ofammonium through the pore. The importance of water forthe stabilization of the protonated NH4

+ ion relative to thedeprotonated NH3 molecule has already been pointed out byBostick and Brooks32,33 and Berneche et al.5,46 Althoughintraluminal water is not observed in most of the MDsimulations reporting the potential of mean force profiles,other MD studies show stable46,49 or transient36,37 hydration ofthe pore lumen. Most notably, a recent MD simulation ofEcAmtB with a polarizable force field also showed stablehydration of the pore.49 Thus, the protein−water interactionsmight be influenced by the chosen water model.101,102 Alongthese lines, a recent work studied the role of the water model inbinding free energy calculations and found that a more detailed5-site water model like the one used here yielded more reliablepredictions than older, three-site water models like those usedin the MD studies that did not show hydration of thehydrophobic pore lumen of EcAmtB.103

The standard binding free energy directly measures thedifference between the interactions of the permeant with theprotein environment and the bulk solvent. Thus, G°,bind can beused to analyze whether AfAmt-1 has an intrinsic selectivity fora certain permeant species over other permeant species. Thestandard binding free energies reveal that AfAmt-1 is selectivefor NH4

+ over H3O+ at the vestibule regions (Am1a, Am1b, and

Am7) and at the center of the pore lumen (Am3 and Am4).This selectivity is based on the higher desolvation penalty for

the smaller and more polar H3O+ ion. In contrast, a selectivity

of AfAmt-1 for NH3 over H2O is not apparent from our results,which is perhaps not surprising given the similar physicochem-ical properties of these molecules. Such a selectivity might,however, also arise from differences in the free energy barriersbetween the permeant positions which are not included in ourcalculations. Binding of the OH− ion is very unfavorablebecause of the high desolvation penalty and the unfavorableelectrostatic interaction with the protein (Figure 4b).The binding free energy extends the standard binding free

energy by adding the effect of the actual activities of thedifferent permeant species (Figure 5b). The binding free energyis more favorable if the permeant is more abundant in therespective solvent phase and less favorable if the permeant isless abundant. The activity of the different protonation forms ofammonia and water is determined by the pH value of therespective solvent phase (see Methods section). At neutral pHvalues, NH4

+ is much more abundant than NH3. Similarly, H2Ois the predominant protonation form of water, whereas H3O

+

and OH− are very rare. Thus, the contribution of the permeantactivity to the binding free energy strongly favors the binding ofNH4

+ over that of NH3 and the binding of H2O over that ofH3O

+ and OH−. In addition, the total activity of the waterspecies will normally be much higher than that of the ammoniaspecies (typically cNH3

+ cNH4+ < 10−3 mol/L while cH2O ≈

55.5 mol/L). Due to its high abundance, the binding of water ismuch more favorable than the binding of any other permeantspecies at all permeant sites. Consequently, the permeant sitesare almost always occupied by water and only occasionally bythe other permeant species. Thus, it seems unlikely that thetransport mechanism of AfAmt-1 involves the binding of more

Figure 6. Protonation free energy for the twin-His motif and the permeants ammonia and water at the transmembrane pore sites as functions of aproton-motive force. Upper block: pmf consists entirely of an electric transmembrane potential. The pH value is set to 7.0 on both membrane sides.Lower block: pmf consists entirely of a transmembrane pH difference. The intracellular pH value is set to 7.0. The extracellular pH value is given by7.0 + pmf/59 mV. For both blocks, the pN is set to 3.0 on both membrane sides.



than one molecule of the permeants ammonia or ammoniumper transporter monomer at the same time. Crystallographicstudies showed residual electron density in the pore lumen ofEcAmtB.16,17,34,35 As noted earlier by Zheng et al.17 andourselves,18 it is impossible to reliably distinguish betweenwater and ammonia as occupants of the permeant sites on thebasis of the experimentally determined electron density.Berneche and co-workers pointed out the importance of thehigh water concentration for the question whether thepermeant sites are occupied by ammonium/ammonia orwater.5,17 These considerations and the findings from ourcalculations argue for water as predominant occupant of thepermeant sites at least for AfAmt-1 and possibly also for itsstructurally highly similar homologues. Plots of the binding freeenergies for all permeant species at all permeant sites as afunction of the pmf components can be found in section F ofthe Supporting Information.Protonation Free Energies of the Permeant Sites and

the twin-His Motif. In this section, we study the protonationfree energies of ammonia and water at the permeant sites andof the twin-His residues. Figure 6 shows plots of theseprotonation free energies as functions of an electric trans-membrane potential or a transmembrane pH gradient. Thesettings chosen in the calculation of the protonation freeenergies are the same as those used in the calculation of thepermeant binding free energies above. The protonation freeenergies of the twin-His residues and of water and ammonia atthe intracellular permeant sites (Am2 to Am7) are only weakly

dependent on the pH gradient because the intracellular pHvalue is constant. The protonation free energies of NH3 andH2O at the extracellular vestibule (Am1a and Am1b) areroughly linearly dependent on the pH gradient. This depend-ence stems from the dependence of the extracellular pH value,and thus of the extracellular proton activity, on the pH gradient.The effect of the electric transmembrane potential on the

protonation free energies arises from its influence on theintrinsic energies of the binding sites and on the protonelectrochemical potentials of the solvent phases. The trans-membrane potential favors the release of protons to the solventphase with the more negative potential and the uptake ofprotons from the solvent phase with the more positivepotential. This is why the transmembrane potential has anqualitatively opposite effect on the protonation free energy ofintracellular and extracellular binding sites. The effect of thetransmembrane potential increases with the distance of thebinding site from the respective outer surface of the protein(Figure 4a). This dependence can be understood from thedifference in the electrostatic potential between the respectivebulk solvent phase and the position of the binding site. A largerelectrostatic potential difference will lead to a larger magnitudeof the energy that is gained or spent in transferring the protonfrom the bulk solvent to the binding site.The protonation free energy of water is less favorable than

the protonation free energy of ammonia at all permeant sites.This difference is mainly caused by the lower intrinsic protonaffinity of water relative to ammonia. An additional

Figure 7. Free energy level scheme for states of the permeant sites and the twin-His motif occurring during different proposals for the permeationmechanism. The species present at the permeant sites (Am1a to Am6) are indicated at the horizontal axis (gray, NH3; blue, NH4

+; white, H2O). Thefree energy of each state is plotted relative to the free energy of the state with all permeant sites occupied by water, H157 adopting the Nϵ-protonated tautomer and H305 adopting the Nδ-protonated tautomer. The energy levels are color coded according to the configuration adopted bythe twin-His motif as defined by the legend. Connecting lines between the free energy levels are just a guide to the eye and do not imply transitionstate energies. The pH is set to 7.0 on both membrane sides. The pN is set to 3.0 on both membrane sides. Δψ is set to −0.12 V. (a) ElectroneutralNH3 uniport; (b) electrogenic NH4

+ uniport not involving protonation state changes of the twin-His motif; (c) electrogenic NH3/H+ symport

involving protonation state changes of the twin-His motif. It is not clear how the restoration of the twin-His motif’s configuration between the lasttwo stages of this mechanistic scheme will occur microscopically. The restoration might involve a transient reprotonation of the twin-His motif,proton transfer along the water molecules in the pore lumen and/or a transient reorientation of the histidine side chains.



contribution arises from the higher desolvation penalty for thesmaller and more polar hydronium ion relative to theammonium ion. The protonation free energy of the permeantsat the vestibular permeant sites (Am1a, Am1b, Am6, and Am7)is much more favorable than at the luminal permeant sites(Am2, Am3, and Am4). The protonation free energy of waterat the luminal permeant sites is so unfavorable that it seemsunlikely that a hydronium ion at the luminal sites is involved inthe conduction mechanism. In contrast, the lower protonationfree energies of ammonia let it seem possible that anammonium ion can be transiently stabilized at the intraluminalpermeant sites. However, the protonation free energies indicatethat the permanent protonation of ammonia is only favorable atthe vestibular permeant sites but not at the intraluminalpermeant sites. This finding is consistent with the findings ofprevious theoretical studies on EcAmtB32,33,36−48 andNeRh5050 and the binding of xenon to the intraluminalpermeant sites of xenon-pressurized AfAmt-1 crystals.18

The twin-His residues are the only titratable sites of theprotein whose protonation probability is strongly dependent onthe binding of ammonia/ammonium to the permeant sites (seeplots in section E of the Supporting Information). Thepossibilities of an active role of the twin-His motif as transientproton acceptor for the substrate ammonium5,17,34,35 or apassive role as hydrogen bond donor to the permeants passingthe pore lumen have been noted earlier.16 The protonation freeenergies of the twin-His residues have small magnitudes overthe whole range of conditions studied. The small free energydifferences between the protonated and deprotonated forms ofthese residues indicate that transient changes between theprotonation states are easily possible. Thus, the twin-His motifcould play an active role in a possible electrogenic conductionmechanism of AfAmt-1. This possibility is investigated furtherin the next section.Thermodynamics of Possible Permeation Mecha-

nisms. For investigating the thermodynamics of possiblepermeation mechanisms, we concentrate on the permeant sitesand the two histidine residues forming the twin His-motif. Weconsidered microscopic states for these sites, while all othersites can freely equilibrate. For the twin-His motif, weconsidered all five thermodynamically viable permutations ofthe histidine protonation forms as depicted in the legend ofFigure 7. We computed the free energy of all states with one ortwo permeants other than water relative to the fully wateroccupied state with the thermodynamically most favorableprotonation form of the twin His motif (H157 singlyprotonated at the Nϵ atom and H305 singly protonated atthe Nδ atom). The full sets of computed relative free energiesof the states are depicted in Figures S26 to S29 of theSupporting Information. Occupation of more than two sites atthe same time by other permeant species than water isthermodynamically very unfavorable and thus unlikely to beinvolved in the permeation mechanism. Figure 7 shows freeenergy profiles for the possible permeation mechanismsconsidered herein. We did not calculate free energy barriersbetween the intermediate states of the permeation mechanism.Potential of mean force profiles for the permeation of NH3 andNH4

+ through EcAmtB are available from MD studies.32,33,48,49

These profiles indicate that the barriers for permeanttranslocation between the permeant sites are small relative tothe overall electrostatic barrier for the permeation of the porelumen by the ammonium ion. Thus, we believe that the

inclusion of these barriers is of minor importance for evaluatingthe thermodynamic viability of the transport mechanisms.The parameters in the calculations were set to standard

values that could be encountered at the membrane ofmicroorganisms. The pH value was set to 7.0 on bothmembrane sides. The electric transmembrane potential wasset to −0.12 V. A transmembrane pH gradient was not appliedbecause its effect on the transport and binding thermodynamicsis much smaller than that of the electric transmembranepotential (see above). Typically, Δψ is also the dominantcomponent of the pmf.1,19,97 The pN value was set to 3.0 onboth membrane sides. Figure 7 shows the free energy profiles ofpossible conduction mechanisms. Taking into account thepermeant concentrations and the electrochemical transmem-brane gradients has a significant effect on the free energyprofiles. For comparison, Figure S30 of the SupportingInformation shows the same free energy profiles at standardtotal concentration of the permeants and at zero electro-chemical transmembrane gradients.Figure 7a shows the electroneutral NH3 uniport mechanism

first proposed in microscopic detail by Khademi et al. on thebasis of the hydrophobicity of the transmembrane pore.16 Thismechanism was supported by previous theoretical studies onEcAmtB32,33,36−48 and NeRh5050 which concentrated on theammonia or ammonium uniport mechanisms. The NH3uniport mechanism does not involve protonation state changesof the twin-His motif. Ammonium is recruited at Am1a anddeprotonated somewhere close to Am1b. The proton is leftbehind in the extracellular phase. The neutral ammoniamolecule permeates the hydrophobic pore lumen consistingof Am2, Am3 and Am4, and is reprotonated with a proton fromthe intracellular phase at Am5. Finally, the ammonium ion isreleased to the intracellular phase. The reasoning for thedeprotonation of NH4

+ at Am1b and its reprotonation at Am5 isbased on the high protonation free energy of ammonia at theintervening intraluminal permeant sites.Figure 7b shows an electrogenic NH4

+ uniport mechanismthat does not involve protonation state changes of the twin-Hismotif (net transport of NH4

+). The ammonium ion is recruitedfrom the extracellular phase at Am1a, permeates the wholetransmembrane pore passing the intermediate permeant sitesand is released from Am7 to the intracellular phase. Thepermeation of the transmembrane pore is associated with anelectrostatic energy barrier of ca. 15 kcal/mol.Figure 7c shows a possible electrogenic NH3/H

+ symportmechanism (net transport of NH4

+). The most importantfeatures of this mechanism have been proposed by Bernecheand co-workers.5 Ammonium is recruited from the extracellularphase at Am1a, loses its hydration shell at Am1b and istransferred to Am2. At Am2, the ammonium ion isdeprotonated by H157. An escape of the NH3 molecule backto the intracellular vestibule might be hindered by thepreferential permeability of the Phe gate for NH4

+ relative toNH3 reported by Berneche and co-workers.5 The protonationof the twin-His motif is stabilized by the hydrogen bondbetween the two central Nδ nitrogen atoms. This hydrogenbond also enables the twin-His motif to easily change betweenthe two protonated configurations (green and blue in Figure 7)via proton transfer between the two central Nδ nitrogen atoms.In this way, the proton is transferred from H157 to H305 at theintracellular side of the pore. The neutral ammonia moleculepermeates the hydrophobic pore lumen and is reprotonated byH305 at Am5. Finally, the ammonium ion is transferred to Am6



and released to the intracellular phase. This mechanism has aslightly lower electrostatic barrier for the permeation of thepore lumen than the NH4

+ uniport mechanism (ca. 12 kcal/mol). As noted by Berneche et al.,5 this mechanism poses theproblem of how to reset the tautomeric forms of the twin-Hisresidues to those occupied initially. The reset could involve atransient reprotonation of the twin-His motif from theintracellular phase. In addition, the restoration might involveproton transfer along the water molecules in the pore lumen ina Grotthuss mechanism and/or a transient reorientation of thehistidine side chains. The uncertainty about the precisemechanism of the reset makes it impossible at present toquantify the size of the associated free energy barrier withconfidence. Based on gas-phase QM calculations, Lamoureux etal. estimate the free energy barrier for this reset to be no largerthan 15 kcal/mol if the reset involves water molecules in thepore and a transiently formed OH−.49 As discussed above, theformation of a OH− ion is thermodynamically very unfavorablewithin the protein environment (see Thermodynamics ofPermeant Binding section). Within our model, the barrier forthe transient formation of the OH− ion would be about 22kcal/mol (Figures S26 and S28 of the Supporting Information).This high free energy barrier might, however, be lowered ifpolarization and quantum effects are explicitly included. A resetmechanism that involves reorientation of the twin-His sidechains is found by Lamoureux et al. to be unlikely because theassociated barrier is larger than 20 kcal/mol.Which transport mechanism is now likely to be operative?

The low overall free energy barrier of 12 kcal/mol associatedwith the electroneutral NH3 uniport mechanism indicates thatthe mechanism is kinetically feasible. An important counterargument against an NH3 uniport as exclusively operativemechanism is the lack of a net thermodynamic driving forceunder physiologically relevant conditions (see Bioenergetics ofTransmembrane Transport section). In contrast, an NH3uniport is even hindered if a physiological pH gradient isapplied in addition to the electric transmembrane potential(Figure 3); that is, ammonia would be exported instead ofimported. With a pH gradient of ΔpH = 1 pH unit, theammonia import would be hindered by 1.3 kcal/mol. Incontrast, an electrogenic transport mechanism involving NH4

+

can be driven by the electric transmembrane potential (Figure3).Amt/Rh proteins of microorganisms, plants and mycorrhizal

fungi seem to be expressed only if the availability of nitrogen,sources is low, i.e., if the ammonium concentration in themedium is low.3,104−107 This finding underlines the necessityfor these life forms to drive the ammonium import by theelectric transmembrane potential as pointed out earlier byourselves and other authors.1,4,14,18 The free energy schemes forthe electrogenic mechanisms indicate a sizable total free energybarrier of 15−18 kcal/mol for the permeation of the transporterpore. The main contribution to this free energy barrier is thecost of the electrostatic desolvation of the ammonium ion upontransfer from the aqueous solvent to the hydrophobic porelumen (12−15 kcal/mol). The desolvation penalty might belowered further when explicitly accounting for electronicpolarization, which is especially significant in the interactionof aromatic residues with NH4

+.49,75 The electrogenicmechanisms seem to be thermodynamically feasible especiallywhen considering the high optimal growth temperature of A.fulgidus of ca. 80 °C.108,109 The similar magnitude of the freeenergy barriers for the electrogenic mechanism considered and

the uncertainty about the free energy barrier associated with thelast step of the NH3/H

+ symport mechanism do not allow us toprefer one of the mechanism on the basis of the free energyprofiles.Although our calculations concentrated on AfAmt-1 and did

not include other homologues, we do believe that manyarguments are transferable to other homologues. This belief isbased on the high structural similarity of Amt and Rh proteinsrevealed by the available crystal structures.13,16−18,35,110,111 Anelectrogenic transport was reported on the basis of experimentson plant19−24 and microbial Amts25−27 and on human Rhproteins30 implying the involvement of NH4

+ as substrate. Inseeming contradiction, an involvement of NH3 as substrate wasimplied by experiments reported for EcAmtB16 and some Rhproteins.28,29,112,113 These experiments indicated an intra-cellular alkalinization accompanying the transport which wasinterpreted to originate from reprotonation of the transportedNH3 in the intracellular phase.16 The significance of thesefindings for the mechanism of Amt/Rh proteins is, however,debated.4,31 As pointed out earlier by Musa-Aziz et al., analkalinization of the intracellular phase occurs already if afraction of the overall imported ammonia/ammonium istransported as neutral ammonia.11,114 In addition, the experi-ments showed that the transport was stimulated by slightincreases in the extracellular pH value while keeping a pH valuewell below the pKa of ammonium. Under these conditions, apH increase will only have a significant effect on the abundanceand availability of NH3 while the abundance of NH4

+ is merelyaffected. Bakouh et al. observed sensitivity of the transportthrough human RhCG to the transmembrane potential and tothe extracellular pH value.30 These finding lead them topropose that NH3 and NH4

+ are directly involved in thetransport mechanism. The function of molecular systems isinherently stochastic. Thus, the mechanistic schemes shown inFigure 7 may be seen as limiting cases. The electroneutral NH3uniport may also contribute to the total permeant flux acrossthe membrane as long as a parallel electrogenic transportsupplies an overall thermodynamic driving force.The prominent role attributed to the twin-his motif in the

proposed NH3/H+ symport mechanism is consistent with the

high degree of its conservation among Amt/Rh pro-teins.2,5,34,115 The histidine residues can in some cases besubstituted by glutamate or aspartate34,115 which might be ableto perform the same function.49 There are, however, also somerare cases as in some Rh proteins where no equivalent of thetwin-His motif is present.12

From our calculations, it can not be excluded that differenttransport mechanisms are operative in different Amt/Rhproteins as advocated by some workers.9,10,116,117 It is, however,also conceivable that the Amt/Rh proteins can support differenttransport modes. The transport mechanism actually operationalwould then depend on the driving force available in a particularsystem. More work is required to gain certainty in this respect.

■ CONCLUSIONS AND OUTLOOKWe investigated the thermodynamics of different possibletransport mechanisms of AfAmt-1. Both, electrogenic andelectroneutral permeation mechanisms were found to bethermodynamically viable. A net transport of substrate acrossthe membrane requires the presence of a thermodynamicdriving force.64,92,93 Microorganisms like A. fulgidus and plantshave to acquire ammonium at low external ammoniumconcentrations.1,14,19,23,95,96 We found that, in this case, the



driving force for the substrate import can only be provided bythe electric transmembrane potential implying an electrogenictransport mode. We computed free energy profiles for differentelectrogenic transport mechanisms and found that NH4

+

uniport and NH3/H+ symport are thermodynamically viable.

Important factors that allow the permeation of the pore lumenby ammonium are the negative electrostatic potential of theprotein and water present in the pore lumen. These factorsalleviate the free energy cost of desolvating the ammonium ionupon transfer from the solvent to the hydrophobic pore lumen.The possible NH3/H

+ symport mechanism involves thegenetically conserved twin-His motif as intermediate acceptorof the cotransported proton. Further experimental andtheoretical work is needed to discern between the differentpossible electrogenic mechanisms and to obtain a deeperunderstanding of their microscopic details. In particular, itwould be interesting to investigate the stoichiometry of protonsand ammonia transported as functions of the physicalconditions such as pH value, electric transmembrane potential,and transmembrane pH gradient. Theoretical methods thatprovide time information could be used to study microscopicdetails of the transport kinetics. Extensions of our microstatedescription to model the kinetics of molecular systems havealready been applied successfully and might be used fruitfully infuture studies of AfAmt-1.58,118−121

The formalism developed herein for the treatment of ligandswith multiple binding forms is generally applicable. Often, theligand itself can occur in multiple protonation forms whichleads to a coupling of the protonation equilibria of both bindingpartners and the receptor−ligand binding equilibrium. Thecoupling of protein−ligand binding equilibria to the proto-nation equilibria of the binding partners occurring in such casesis currently receiving increasing attention.57,122−134 Ourapproach is thus also interesting within a wider scope ofbinding free energy calculations in general, for example incombination with a constant pH λ-dynamics method.135−137

■ ASSOCIATED CONTENT

*S Supporting InformationParameters used in the simulations, derivations of expressionsfor the chemical potentials and the transfer free energies of theinvestigated permeants, and addititional figures referenced inthe text. This material is available free of charge via the Internetat http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected]; [email protected]; [email protected].

NotesThe authors declare no competing financial interest.

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